Biology Spl

Yes, you are eligible for this. As a minimum criterion of eligibility, you need to have completed graduation in Science (B.Sc) stream from a recognized university with Physics, Chemistry and Biology, as main subjects, and with a minimum aggregate score of 45%.

Yes, for the first two years, you have to take courses in Physics, Chemistry, Biology, Mathematics, and Earth Science. I don't think that it's a problem even if you don't have biology in class 12th, the faculty at IISER-Pune is aware of this and are more than capable of accounting for it. Don't be surprised if, at the end of two years, you end up loving biology.

Thoroughly revise the B.Sc course according to the given syllabus.

If you want to do MBA then don't waste your time in B.Sc. Simply do BBA and if you are interested in science then go for B.Sc & M.Sc. Simply follow your interest, be the best and you will get the job (this rule applies to everyone and every subject).

Non circuit branches will work like civil, environmental engineering, biotechnology.

Yes, you have the prequisite marks for pursuing B.Sc nursing. Go ahead.
All the best.